Slip boundary conditions in nanofluidics from the molecular theory of solvation

Authors: A.E. Kobryn, A. Kovalenko

Affilation: National Institute for Nanotechnology, Canada

Pages: 428 - 431

Keywords: slip boundary conditions, molecular theory of solvation

Abstract:We propose the first-ever derivation and calculation of the hydrodynamic slip length from the first principles of statistical mechanics, based on a combination of linear response theory and equilibrium molecular theory of solvation. The slip length obtained is independent of the type of flow and is related to the fluid organization near the solid surface, as governed by the solid-liquid and liquid-liquid interaction. In the wide range of shear rates and surface-liquid interactions, the slip length is expressed in terms of the Green-Kubo-Nakano relations as a function of the anisotropic inhomogeneous time correlation function of density fluctuations of the liquid in contact with the surface. We derive generic analytical expressions for the liquid-surface friction coefficient (and slip length) for an arbitrary surface-liquid interaction potential. We further illustrate it by numerical calculations for the case of a laminar flow of nine molecular liquids at ambient conditions in contact with the (100) FCC surface of gold, copper and nickel modeled by using all-atom or united-atom models for liquids and the Steele potential for crystalline surfaces. The obtained values for slip length range from few to hundreds of nanometers and are consistent with experimental measurements.